The visitors had gone behind to Frenchman David Friio's near-post header on the hour before Cooper was tripped by Peter Gilbert for a penalty, which Carl Cort converted.
Moments after the restart, Cooper leapt into Gilbert, clattering the young full-back with such force that he had to be stretchered off.
While Argyle were still coming to terms with the loss of their lead and Gilbert's misfortune, Wolves' other substitute, Dean Sturridge, nipped in behind the Pilgrims defence to net a winner.
The defeat was Argyle's second at Home Park in a week and was ill deserved. Midfielder David Norris saw a shot canon back off a post immediately after Friio's opener, and Paul Wotton was also denied by the woodwork in the dying minutes.
Wolves wasted an opportunity to open the scoring just after the interval when Paul Ince played in Shaun Newton, who dragged his shot across the face of Romain Larrieu's goal.
Nigerian midfielder Seyi Olofinjana then headed Mark Clyde's cross wide of the post before Argyle took the lead when Friio headed home Gilbert's cross.
The visitors levelled with 13 minutes to go when Gilbert ran into the back of Cooper as he bore down on goal. It was a definite penalty, which Cort converted by putting the ball to the wrong side of Larrieu.